Question

Express in Slope-Intercept Form

Answer 1

y = 3/4x + 2

Explanation:

We only need to find two components,

m and b (slope and y intercept)

Let's find b first because it is easy.

From the line, it passes the y axis through point (0,2) or 2

So b = 2

y = __x + 2

Slope:

Find any two points from the line. (Must be a clear coordinate)

I'll pick,

(-4,-1) and (0,2)

Slope formula:

m = y₂ - y₁ / x₂ - x₁

m = 2 -(-1) / 0 -(-4)

m = 2 + 1 / 0 + 4

m = 3/4

Now that we have the slope, we have completed the slope-intercept form.

y = 3/4x + 2

Answer 2

y = (3/4)x + 2

Explanation:

Slope-intercept form is y=mx+b where (x, y) is a point on the linear graph, m is the slope (rise/run), and b is the y-intercept (the y-value at which the graph passes through the y-axis).

Looking at the graph, we can see that the point at which the line crosses the y-axis is (0, 2) which makes it the y-intercept. Thus, the b in the slope-intercept form is 2.

Next, we are looking for the slope of the line. To do this, we can calculate the rise/run of the line by choosing to points on it. Since we already have the point (0, 2), we just need one more.

For example, the point (-4, -1) can be used. The slope can be found by ((y-y)/(x-x)) in which the first y and x values correspond with the first point and that of the second correspond with the second set. So in this case, m = (2-(-1))/(0-(-4)) = 3/4

Plugging in the calculated m and b value in the slope intercept equation, we get y = (3/4)x + 2