(-4,6); 2y = 3x -6 ?

Question

Write the SLOPE-INTERCEPT FORM of the equation of the like that passes through the given point and PARALLEL to the graph of the equation.

Answer 1

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

The equation is 2y = 3x - 6.

Divide each side by 2.

y = 3/2x - 3.

Compare the equation with slope-intercept form y = mx + b.

slope = 3/2 and y-intercept is - 3.

y-intercept is - 3, so the line crosses the y-axis at (0, - 3)

Using slope find the next point.

Slope = rise/run = 3/2

Start at point (0, - 3), move 3 units up and 2 units right, then plot the point (2, 0).

Point _ slope form is y - y1 = m(x - x1).

Say the point (x1, y1) = (- 4, 6) and slope (m) = 3/2.

The line is y - 6 = 3/2(x + 4)

y = 2/3x + 12.

Compare the equation with slope-intercept form y = mx + b.

slope = 3/2 and y-intercept is 12.

y-intercept is 12, so the line crosses the y-axis at (0, 12)

Using slope find the next point.

Slope = rise/run = 3/2

Start at point (0, 12), move 3 units up and 2 units right, then plot the point (2, 15).

Draw two lines through these points.

Graph :

From the graph,the lines are parallel lines.