Question

Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5

Answer 1

slope-intercept:
`y=(-4)/(5) x-(2)/(5)`

point-slope:
`y-2=(-4)/(5) (x+3)`

Explanation:

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.

Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:

y - y1 = m(x - x1)

y - 2 = (-4/5) * (x + 3)

`y-2=(-4)/(5) (x+3)`

Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:

y = mx + b

y = (-4/5)x + b

Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:

y = (-4/5)x + b

2 = (-4/5) * (-3) + b

2 = 12/5 + b

b = -2/5

So, the y-intercept is -2/5. Then the slope-intercept form is:

`y=(-4)/(5) x-(2)/(5)`

Thus, our two equations are:

slope-intercept:
`y=(-4)/(5) x-(2)/(5)`

point-slope:
`y-2=(-4)/(5) (x+3)`