The equation for line s can be written as y= – 10x+ 5 4 . Parallel to line s is line t, which passes through the point ( – 1,3). What is the equation of line t?

Question

Bytelearn · Accepted Answer

Find Slope of Line s: Determine the slope of line s. Line s has the equation y = –10x + 5/4. The slope of a line in the form y = mx + b is m, where m is the coefficient of x. The slope of line s is -10.Parallel Lines Slope: Since line t is parallel to line s, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line t is also -10.Point-Slope Form: Use the point-slope form to find the equation of line t. The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know the slope (m) is -10 and the point (x1, y1) is (-1, 3).Plug Slope and Point: Plug the slope and point into the point-slope form equation. y - 3 = -10(x - (-1)) y - 3 = -10(x + 1)Distribute Slope: Distribute the slope on the right side of the equation. y - 3 = -10x - 10Isolate y: Isolate y to put the equation in slope-intercept form. Add 3 to both sides of the equation. y = -10x - 10 + 3 y = -10x - 7Verify Equation Form: Verify that the equation is in slope-intercept form and simplified. The equation y = -10x - 7 is in the form y = mx + b, where m is the slope and b is the y-intercept. The equation is simplified and in the correct form.

The equation for line $s$ can be written as $y= -10x+ \frac{5}{4}$ . Parallel to line $s$ is line $t$ , which passes through the point $(-1,3)$ . What is the equation of line $t$ ?

Full solution

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

Related topics

The equation for line sss can be written as y=−10x+54y= -10x+ \frac{5}{4}y=−10x+45​. Parallel to line sss is line ttt, which passes through the point (−1,3)(-1,3)(−1,3). What is the equation of line ttt?

The equation for line $s$ can be written as $y= -10x+ \frac{5}{4}$ . Parallel to line $s$ is line $t$ , which passes through the point $(-1,3)$ . What is the equation of line $t$ ?