Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Line ss has an equation of y=−710x−1y = -\frac{7}{10}x - 1. Line tt, which is parallel to line ss, includes the point (−6,5)(-6,5). What is the equation of line tt?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write an equation for a parallel or perpendicular lineright chevron icon

Full solution

Q. Line ss has an equation of y=−710x−1y = -\frac{7}{10}x - 1. Line tt, which is parallel to line ss, includes the point (−6,5)(-6,5). What is the equation of line tt?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Find Slope of Line ss: Determine the slope of line ss. Line ss has an equation of y=−710x−1y = -\frac{7}{10}x - 1. The slope of a line in the form y=mx+by = mx + b is mm, where mm is the coefficient of xx. The slope of line ss is −710-\frac{7}{10}.
  2. Determine Slope of Line tt: Since line tt is parallel to line ss, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line tt is also −710-\frac{7}{10}.
  3. Use Point-Slope Form: Use the point-slope form to find the equation of line tt. The point-slope form of a line is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. We know the slope (mm) is −710-\frac{7}{10} and the point (x1,y1)(x_1, y_1) is (−6,5)(-6, 5). Plugging these values into the point-slope form gives us y−5=−710(x−(−6))y - 5 = -\frac{7}{10}(x - (-6)).
  4. Convert to Slope-Intercept Form: Simplify the equation from point-slope form to slope-intercept form.\newlineFirst, distribute the slope −710-\frac{7}{10} across (x+6)(x + 6).\newliney−5=−710×x−(−710×6)y - 5 = -\frac{7}{10} \times x - (-\frac{7}{10} \times 6)\newliney−5=−710×x+710×6y - 5 = -\frac{7}{10} \times x + \frac{7}{10} \times 6\newlineNow, simplify 710×6\frac{7}{10} \times 6.\newline710×6=4210=4.2\frac{7}{10} \times 6 = \frac{42}{10} = 4.2 or 215\frac{21}{5} in fraction form.\newlineSo, y−5=−710×x+215y - 5 = -\frac{7}{10} \times x + \frac{21}{5}
  5. Final Equation of Line t: Add 55 to both sides of the equation to solve for yy.\newliney=−710⋅x+215+5y = -\frac{7}{10} \cdot x + \frac{21}{5} + 5\newlineNow, convert 55 to a fraction with a denominator of 55 to combine with 215\frac{21}{5}.\newline5=2555 = \frac{25}{5}\newlineSo, y=−710⋅x+215+255y = -\frac{7}{10} \cdot x + \frac{21}{5} + \frac{25}{5}\newlineCombine the fractions.\newliney=−710⋅x+465y = -\frac{7}{10} \cdot x + \frac{46}{5}\newlineThis is the equation of line tt in slope-intercept form.

More problems from Write an equation for a parallel or perpendicular line

Question
Does the point (0,4)(0, 4) satisfy the equation y=xy = x??
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the slope of the line y=−4x+25 y = -4x + \frac{2}{5} .
Get tutor helpright-arrow

Posted 8 months ago

Question
Rewrite the following equation in slope-intercept form.\newliney+8=−8(x−10)y + 8 = -8(x - 10)
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the y y -intercept of the line 14x−16y=−10 14x - 16y = -10 .\newlineWrite your answer as an integer or decimal or fraction, not as an ordered pair.
Get tutor helpright-arrow

Posted 8 months ago

Question
Line q q has a slope of −23 \frac{-2}{3} . Line r r is perpendicular to q q . What is the slope of line r r ?
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the slope of the line y+3=−118(x+6)y + 3 = -\frac{1}{18}(x + 6).\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
Line p p has an equation of y=−8x+6 y = -8x + 6 . Line q q , which is perpendicular to line p p , includes the point (2,−2) (2, -2) . What is the equation of line q q ??\newlineWrite the equation in slope-intercept form.
Get tutor helpright-arrow

Posted 8 months ago

Question
Is the graph of this equation a horizontal or vertical line?\newlinex=7x = 7
Get tutor helpright-arrow

Posted 8 months ago

Question
Determine the standard form of the following equation:\newliney=−10x+7 y = -10x + 7
Get tutor helpright-arrow

Posted 8 months ago

Question
A line with a slope of 99 passes through the point (9,9)(9,9). What is its equation in point-slope form?
Get tutor helpright-arrow

Posted 8 months ago

View all (101)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant