Final answer:
To find the equation of a line with a vertex of (-6, -4) and going through x-axis at x = -4, we use the slope formula and the coordinates of the vertex. The slope is found by taking the difference in y-values and dividing by the difference in x-values. The equation of the line is y = 2x + 8, and the y-intercept is 8.
Step-by-step explanation:
To find the equation of a line that has a vertex of (-6, -4) and goes through the x-axis at x = -4, we first need to find the slope of the line. The slope can be determined by finding the difference in the y-values of the two points. Since the vertex (-6, -4) is on the line and it goes through the x-axis at x = -4, we can use these two points to find the slope. The slope is given by (change in y)/(change in x) = (-4 - 0)/(-6 - -4) = -4/-2 = 2.
The equation of the line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Now that we know the slope (m = 2), we can substitute this value, along with the coordinates of the vertex (-6, -4), into the equation and solve for b. -4 = 2(-6) + b, which simplifies to -4 = -12 + b. Adding 12 to both sides, we get 8 = b.
Therefore, the equation of the line is y = 2x + 8. The y-intercept is 8.