Question

problem 10. (1 point)
find an equation for of each of the lines in the figure.
line a (in red) has equation ( y=) help (formulas)
line b (in blue) has equation ( y=) help (formulas)
note: you can earn partial credit on this problem

Explanation:

Step1: Find the slope and y - intercept for Line A

Line A passes through the point \((0,1)\) (y - intercept \(b = 1\)). Let's assume another point on Line A. Since it's a straight line, we can use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). But wait, looking at the graph, for Line A (red line), we can use the fact that the equation of a line is \(y=mx + b\). From the graph, when \(x = 0\), \(y=1\) (so \(b = 1\)). Let's find the slope. Suppose two points \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(0.5,0)\) (by visual inspection of the grid). Then \(m=\frac{0 - 1}{0.5-0}=- 2\). So the equation of Line A is \(y=-2x + 1\).

Step2: Find the slope and y - intercept for Line B

Line B passes through the point \((0,1)\) (y - intercept \(b = 1\)). Let's take two points on Line B. For example, \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(1,1.5)\) (by visual inspection of the grid). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1.5 - 1}{1-0}=0.5=\frac{1}{2}\). So the equation of Line B is \(y=\frac{1}{2}x+1\).

Answer:

Line A: \(y=-2x + 1\); Line B: \(y=\frac{1}{2}x + 1\)