Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.
a. This is a nonlinear function. Its graph is a curve.
b. This is a nonlinear function. Its graph has a maximum at (0,10).
c. This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.
d. This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
d. This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
In this equation, y is equal to -4 times x plus 10. This is in the form of y = mx + b, which is the standard form for a linear equation. The slope of -4 tells us that the line will decrease by 4 units for every 1 unit increase in x. The y-intercept of 10 tells us that the line will intersect the y-axis at the point (0,10).
When graphed, this linear function will be a straight line that slants downward from left to right, with a y-intercept of 10.