How do you find where a liine intercepts another point on a graph.

Question

Line y=2/3x+13.5 and Line y=-1/2x+3
where do they intersect?
thank you.

Answer 1

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

The first equation is y = (2/3)x + 13.5.

It is already in slope intercept form.

So,compare the equation with slope-intercept form y = mx + b.

slope = 2/3 and y-intercept is 13.5.

y-intercept is 13.5, so the line crosses the y-axis at (0, 13.5)

Using slope find the next point.

Slope = rise/run = 2/3

Start at point (0, 13.5), move 2 units up and 3 units right, then plot the point (3, 15.5).

The second equation is y = (- 1/2)x + 3.

It is already in slope intercept form.

So,compare the equation with slope-intercept form y = mx + b.

slope = - 1/2 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 = - 1/2

Start at point (0, 3), move 1 unit down and 2 units right, then plot the point (2, 2).

Draw the lines through these points.

Graph :

Observe the graph, the intersect point is (x, y) = (- 9, 7.5).