Graphing equations quick check.

Question

(0,-4) (1,-1)
using the graph, derive the equation of the line in slope-intercept form.

Answer 1

First, let's calculate the slope of the line using the two given points.

slope = (y2 - y1) / (x2 - x1)
slope = (-1 - (-4)) / (1 - 0)
slope = (3) / (1)
slope = 3

Now that we have the slope, let's use the point-slope form of the equation of a line to find the equation in slope-intercept form.

y - y1 = m(x - x1)
y - (-4) = 3(x - 0)
y + 4 = 3x

Now, let's rewrite the equation in slope-intercept form by isolating y:

y = 3x - 4

Therefore, the equation of the line in slope-intercept form is y = 3x - 4.

Answer 2

(0,1), (1,-4)
Write the equation of the line in slope-intercept form.

Answer 3

We will first calculate the slope using the given points.

slope = (y2 - y1) / (x2 - x1)
slope = (-4 - 1) / (1 - 0)
slope = -5 / 1
slope = -5

Now that we have the slope, we will use the point-slope form of the equation of a line to find the equation in slope-intercept form.

y - y1 = m(x - x1)
y - 1 = -5(x - 0)
y - 1 = -5x

Now, we will rewrite the equation in slope-intercept form by isolating y:

y = -5x + 1

Therefore, the equation of the line in slope-intercept form is y = -5x + 1.