Question

check your understanding
practise

1. what are the slope and y-intercept of each line?

a) $y = -5x + 4$
b) $y = \frac{3}{4}x + 1$
c) $y = x - 7$
d) $y = -4x$
e) $y = -3$
f) $y = 0.5x - 1.25$

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept (the point $(0, b)$). For horizontal lines ($y = k$), slope $m=0$ and y-intercept is $(0,k)$.

Step2: Analyze part (a)

For $y = -5x + 4$, match to $y=mx+b$:
$m = -5$, $b = 4$

Step3: Analyze part (b)

For $y = \frac{3}{4}x + 1$, match to $y=mx+b$:
$m = \frac{3}{4}$, $b = 1$

Step4: Analyze part (c)

For $y = x - 7$, rewrite as $y = 1x - 7$, match to $y=mx+b$:
$m = 1$, $b = -7$

Step5: Analyze part (d)

For $y = -4x + 0$, match to $y=mx+b$:
$m = -4$, $b = 0$

Step6: Analyze part (e)

For $y = -3$, rewrite as $y = 0x - 3$, match to $y=mx+b$:
$m = 0$, $b = -3$

Step7: Analyze part (f)

For $y = 0.5x - 1.25$, match to $y=mx+b$:
$m = 0.5$, $b = -1.25$

Answer:

a) Slope: $-5$, y-intercept: $(0, 4)$
b) Slope: $\frac{3}{4}$, y-intercept: $(0, 1)$
c) Slope: $1$, y-intercept: $(0, -7)$
d) Slope: $-4$, y-intercept: $(0, 0)$
e) Slope: $0$, y-intercept: $(0, -3)$
f) Slope: $0.5$, y-intercept: $(0, -1.25)$