Question

Here is an equation: 2x+3y+4=10.

a) Show that this is the equation of a straight line with a gradient of -2/3.

b) Work out the y-intercept

Answer 1

We can rewrite the line in slope-intercept form (i.e., y = mx + b), where m is the slope/gradient and b is the y-intercept.

Thus, we need to isolate y in the equation we're given:

`2x+3y+4=10\\2x+3y=6\\3y=-2x+6\\y=-2/3x+2`

Thus, the gradient is -2/3 and the y-intercept is 2. As a point, the y-intercept is (0, 2)

If you're teacher requires you to have another way to find the intercept, you can remember that at the y-intercept, x =0. Thus, you can find the y-intercept with the original equation by simply plugging in 0 for x and solving for y:

`2(0)+3y+4=10\\3y+4=10\\3y=6\\y=2`