Answer:
y = 4x + 34
Explanation:
To find an equation in slope-intercept form that passes through the point (-9, -2) and is parallel to the graph of the equation y = 4x + 2, we can use the fact that parallel lines have the same slope.
Since the given equation has a slope of 4, our parallel line will also have a slope of 4.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
Substituting the values (-9, -2) and m = 4, we get:
y - (-2) = 4(x - (-9))
Simplifying the equation gives us:
y + 2 = 4(x + 9)
Expanding further:
y + 2 = 4x + 36
To write the equation in slope-intercept form, we isolate y:
y = 4x + 36 - 2
Simplifying gives us:
y = 4x + 34
Therefore, the equation in slope-intercept form that passes through the point (-9, -2) and is parallel to the graph of y = 4x + 2 is y = 4x + 34.