(1, 3) (0, -2) Use the graph to derive the equation of the line in slope interact form

Answer 1

To find the equation of the line in slope-intercept form, we need to determine the slope of the line and the y-intercept.

From the graph, we can see that the line passes through the points (1, 3) and (0, -2).

The slope of the line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (-2 - 3) / (0 - 1)
m = -5 / -1
m = 5

Now that we have the slope, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the point (1, 3):

y - 3 = 5(x - 1)

Expanding:

y - 3 = 5x - 5

Now, rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

y = 5x - 5 + 3
y = 5x - 2

Therefore, the equation of the line in slope-intercept form is y = 5x - 2.

Answer 2

Use the table to answer the question

x y
-5 0
0 5
2 7

Which linear equation represents this non proportional linear relationship

Answer 3

To find the linear equation that represents the non-proportional linear relationship in the table, we need to first calculate the slope of the line using two of the given points.

Let's use the points (0, 5) and (2, 7) to calculate the slope:

m = (y2 - y1) / (x2 - x1)
m = (7 - 5) / (2 - 0)
m = 2 / 2
m = 1

Now that we have the slope, we can pick one of the points to use in the point-slope form of the equation of a line:

Using the point (0, 5):
y - y1 = m(x - x1)
y - 5 = 1(x - 0)
y - 5 = x

Rearranging the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

y = x + 5

Therefore, the linear equation representing the non-proportional linear relationship in the table is y = x + 5.