Find an equation of the line that satisfies the given conditions.
Through
(−7, −12);
perpendicular to the line passing through
(−4, 0) and (0, −2)
the slope of the given line is -1/2
so, the slope of perpendiculars is +2
So, the line you want is
y+12 = 2(x+7)
I really need to help with this
To find the equation of a line perpendicular to another line, we need to first find the slope of the given line. We can use the formula for slope:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are two points on the line.
Using the points (-4, 0) and (0, -2) on the given line, we can calculate the slope:
m = (-2 - 0) / (0 - (-4))
= -2 / 4
= -1/2.
Since the line we are looking for is perpendicular to the given line, the slope of the line we are looking for will be the negative reciprocal of -1/2, which is 2.
So, the line we are looking for has a slope of 2. We can now use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) is the point (-7, -12) and m is the slope.
Plugging in the values, we get:
y - (-12) = 2(x - (-7)).
Simplifying,
y + 12 = 2(x + 7).
Expanding,
y + 12 = 2x + 14.
Rearranging,
y = 2x + 2.
Therefore, the equation of the line that satisfies the given conditions is y = 2x + 2.
To find the equation of the line, we need to determine both the slope and the y-intercept.
Step 1: Find the slope of the given line passing through (-4, 0) and (0, -2).
The formula for finding the slope, m, between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Applying this formula:
slope = (-2 - 0) / (0 - (-4))
= -2 / 4
= -1/2
So, the slope of the given line is -1/2.
Step 2: Determine the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.
The slope of the perpendicular line would be the opposite sign and the reciprocal of the given slope of -1/2.
So, the slope of the perpendicular line = -1 / (-1/2) = 2
Step 3: Use the point-slope form of the equation to find the equation of the line passing through (-7, -12) with a slope of 2.
The point-slope form of the equation is:
y - y1 = m(x - x1)
Substituting the given point (-7, -12) and the slope m = 2 into the equation:
y - (-12) = 2(x - (-7))
y + 12 = 2(x + 7)
Simplifying the equation:
y + 12 = 2x + 14 (distributed 2 to x and 7)
y = 2x + 14 - 12 (moved 12 to the right side)
y = 2x + 2 (simplified)
Therefore, the equation of the line that satisfies the given conditions is y = 2x + 2.