Question

3 determine the equation of the line with the same slope as $y = 6x - 5$ and that has the same x-intercept as the line defined by the equation $2x - 4y + 8 = 0$.

Explanation:

Step1: Identify target slope

The slope of $y=6x-5$ is $m=6$.

Step2: Find x-intercept of given line

Set $y=0$ in $2x-4y+8=0$:
$$2x - 4(0) + 8 = 0$$
$$2x = -8$$
$$x = -4$$
The x-intercept is the point $(-4, 0)$.

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute $m=6$, $x_1=-4$, $y_1=0$:
$$y - 0 = 6(x - (-4))$$
$$y = 6(x + 4)$$

Step4: Simplify to slope-intercept form

$$y = 6x + 24$$

Answer:

$y = 6x + 24$