Answer:
y = 4x + 3
Step-by-step explanation:
as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:
to calculate for the y intercept, it is best to express the equation in slope intercept form:
y = mx + b
in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).
y = 4x + b
what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.
Using this information, we can replace x and y in the equation:
-5 = 4(-2) + b
with consideration to the order of operations, it is important to solve the brackets first
-5 = -8 + b
now to get b by itself add 8 to both sides of the equation:
-5 + 8 = -8 + 8 + b
3 = b
now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.
y = 4x + b
replace b with the number we solved for (3).
y = 4x + 3
this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)
hope this helps :)
