Final Answer:
The equation y = 2x + 10 has slope 2 and passes through (-4,2).
Step-by-step explanation:
To write the equation of a line with a given slope and passing through a certain point, we can use the point-slope form of the equation of a line, which is expressed as:
y - y₁ = m(x - x₁)
Where:
m is the slope of the line.
(x₁, y₁) is the point through which the line passes.
In this particular case, we are given a slope m of 2 and a point (x₁, y₁) of (-4, 2).
Substituting these values into the point-slope form, we get:
y - 2 = 2(x - (-4))
Let's simplify the equation further:
y - 2 = 2(x + 4)
y - 2 = 2x + 8
Now, we'll solve for y to put the equation in slope-intercept form, which is y = mx + b, where b is the y-intercept of the line.
y = 2x + 8 + 2
y = 2x + 10
So, the equation of the line in slope-intercept form is:
y = 2x + 10
This is the final simplified equation of the line with a slope of 2 that passes through the point (-4, 2).