Question

A line goes through the points (8,9) and (-2,4).

Answer 1

Part A:

Slope of line is given by vertical distance ÷ horizontal distance

Let (8, 9) be (x₁, y₂) and (-2, 4) be (x₂, y₂)
The vertical distance is y₂ - y₁ = 4 - 9 = -5
The horizontal distance is x₂ - x₁ = -2 - 8 = -10

slope of the line = -5 ÷ -10 = 0.5
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Part B

The point-slope form is given by
(y - y₁) = m (x - x₁)

We have the gradient, m = 0.5
(x₁, y₁) = (8, 9) ⇒ You can also use the other coordinate (-2, 4)
Substitute these value into the form, we have

(y - 9) = 0.5 (x - 8)
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Part C

The slope-intercept form is given by the equation
y = mx + c

Where m is the slope gradient and c is the point where the line intercepts the y-axis. We don't have the value of c at the moment but we can find out by simplifying the equation in part B

y - 9 = 0.5 (x - 8) ⇒ Multiplying out the bracket
y - 9 = 0.5x - 4
y = 0.5x - 4 + 9
y = 0.5x + 5 ⇒ This the slope-intercept form

Answer 2

You're answer should be (B) hopes it helps.