Find the sum of f(4) + g(-5) when f(x) = 4x - 3 and g(x) = -2x + 10
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Answer:
y = 4
Step-by-step explanation:
Given the equation of the line, y = 6, passing through point (3, 4):
By definition, parallel lines have the <u>same slope</u>.
The linear equation, y = 6 is a horizontal line with a zero slope. Therefore, the parallel line must also have the same slope = 0.
Plug the given values from the point (3, 4) into the slope-intercept form:
y = mx + b
where: y = 4, m = 0, and x = 3. We need to solve for the y-intercept, b:
y = mx + b
4 = 0(3) + b
4 = 0 + b
4 = b
Therefore, the y-intercept is (0, 4).
For horizontal lines, the y-coordinate = 4 stays the same, while having different x-coordinates.
Therefore, the equation that is parallel to y = 6 is y = 4.
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It's a linear function. The graph is a straight line, therefore we need only two points.
Select any value of x and calculate the value of y:
y = -3x + 4
for x = 0 → y = -3(0) + 4 = 4 → (0, 4)
for x = 2 → y = -3(2) + 4 = -2 → (2, -2)
