Question

Graph the line formed by the x-intercept, 5, and y-intercept, 10. Identify the slope (m) and y-intercept (b). Write the slope-intercept equation of the line (y = mx + b).

a) Slope (m) = 2, Y-intercept (b) = 10, Equation: y = 2x + 10
b) Slope (m) = 5, Y-intercept (b) = 10, Equation: y = 5x + 10
c) Slope (m) = 10, Y-intercept (b) = 5, Equation: y = 10x + 5
d) Slope (m) = 10, Y-intercept (b) = 2, Equation: y = 10x + 2

Answer 1

The line with an x-intercept of 5 and a y-intercept of 10 has a slope of -2 and a y-intercept of 10, leading to the slope-intercept equation y = -2x + 10, which is an option (a).

Step-by-step explanation:

To graph the line with an x-intercept of 5 and a y-intercept of 10, we plot the points (5,0) and (0,10) on a coordinate plane and draw a line through these points. The slope (m) of the line can be found by calculating the change in y divided by the change in x, also known as 'rise over run'. In this case, the slope would be (0-10)/(5-0) = -10/5, which simplifies to -2. The y-intercept (b) is already given as 10 because the line crosses the y-axis at (0,10).

Thus, we can write the slope-intercept equation of the line as y = mx + b, which in our case becomes y = -2x + 10. Clearly, this corresponds to option (a) as the correct choice: Slope (m) = -2, Y-intercept (b) = 10, Equation: y = -2x + 10.