The equation of line g is y = 6x - 7. Line h, which is parallel to line g, includes the point (1,1). What is the equation of line h? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. ______

Question

The equation of line g is y = 6x - 7. Line h, which is parallel to line g, includes the point (1,1). What is the equation of line h? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.   ______

Bytelearn · Accepted Answer

Determine Slope of Line: Determine the slope of line g. The equation of line g is given as y = 6x - 7. This equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Therefore, the slope of line g is 6.Find Parallel Line Slope: Since line h is parallel to line g, it must have the same slope. Parallel lines have identical slopes. Therefore, the slope of line h is also 6.Use Point-Slope Form: Use the point-slope form to find the equation of line h. 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 that line h passes through the point (1,1) and has a slope of 6. Plugging these values into the point-slope form gives us the equation of line h.Substitute Values: Substitute the known values into the point-slope form equation. Using the point (1,1) and the slope 6, the equation becomes y - 1 = 6(x - 1).Simplify Equation: Simplify the equation to get it into slope-intercept form. To simplify, distribute the slope 6 on the right side of the equation: y - 1 = 6x - 6 Now, add 1 to both sides to solve for y: y = 6x - 6 + 1 y = 6x - 5Write Final Equation: Write the final equation of line h in slope-intercept form. The equation of line h in slope-intercept form is y = 6x - 5.

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