Question

The graph of the line y = mx + b is sketched below. Use the graph to find m and b.

-
10 -8 -6 4/2
The slope m =
b =
10+
8
6-
4
2
-2-
-4
-6-
-8
-10+
-~
2
4 6 8 10

Answer 1

An equation in slope-intercept form that represents the relationship shown on the graph is y = 3/2(x) + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

First of all, we would determine the slope for this table by using these points (2, 6) and (-2, 0);

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) = (0 - 6)/(-2 - 2)

Slope (m) = -6/-4

Slope (m) = 3/2

At data point (-2, 0) and a slope of 3/2, an equation for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y - 0 = 3/2(x + 2)

y = 3/2(x) + 3