Answer:
x-intercept at (2, 0); y-intercept at (0, ³/₂)
Explanation:
(a) Slope
The point-slope formula for a straight line is
y₂ - y₁ = m(x₂ - x₁)
The line goes through the points (6, -3) and (14, -9).
-9 – (-3) = m(14 – 6)
-6 = -8m
m = -⁶/₈
m = -¾
(b) Equation of line
y = mx + b
Use the point (6, -3)
-3 = -¾ ×6+ b
-3 = -¹⁸/₄ + b
-3 = -⁹/₂ + b
Add ⁹/₂ to each side
b = -3 + ⁹/₂
b = -⁶/₂ + ⁹/₂
b = ³/₂
∴ y = -¾x + ³/₂
(c) y-intercept
Let x = 0.
y = -¾(0) + ³/₂ = 0 + ³/₂ = ³/₂
The y-intercept is at (0, ³/₂).
(d) x-intercept
Let y = 0.
0 = -¾x + ³/₂
Multiply each side by 4
0 = -3x + 6
Subtract 6 from each side
-6 = -3x
Divide each side by -3
x = 2
The x intercept is at (2, 0).
The insert below shows the graph with the intercepts at (2,0) and (0, ³/₂)