Question

Identify the straight-line equation for the graph below: P1 4 y 3 2 D -3.0 -2.0 -1.0 СО 1 -2 3 P2 10 2.0 3.0 Plot of straight line passing through co-ordinates p₁ (-3, 3) and p² (1, 0)​

Answer 1

The straight-line equation for the graph that passes through p₁ (-3, 3) and p² (1, 0)​ is: y = -3/4x + 3/4.

What is the straight-line equation?

To find the equation of the straight line passing through points
`\(P_1(-3, 3)\)` and
`\(P_2(1, 0)\)`, you can use the slope-intercept form of the equation for a line:

y = mx + b.

First, calculate the slope (m) using the formula:

`\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}.\]`

For the points
`\(P_1(-3, 3)\)` and
`\(P_2(1, 0)\)`:

`\[m = \frac{{0 - 3}}{{1 - (-3)}} = \frac{{-3}}{{4}}.\]`

Now that you have the slope (m), you can use one of the given points to find the y-intercept (b). Let's use
`\(P_1(-3, 3)\)`:

`\[3 = \frac{{-3}}{{4}} \cdot (-3) + b.\]`

Solving for b:

3 = 9/4 + b

b = 3 - 9/4

b = 3/4

Now, you have the slope (m = -3/4) and the y-intercept (b = 3/4), so the equation of the line is:

y = -3/4x + 3/4.