The graph of a line in the xy-plane has a slope of 1 and contains the point (3,0). The graph of a second line has a slope of -(1)/(4) and contains the point (-7,0). If the two lines intersect at the point (a,b), what is the value of a+b ? Choose 1 answer: (A) -8 (B) -5 (C) -2 (D) -1

Question

The graph of a line in the  xy-plane has a slope of 1 and contains the point  (3,0). The graph of a second line has a slope of  -(1)/(4) and contains the point  (-7,0). If the two lines intersect at the point  (a,b), what is the value of  a+b ? Choose 1 answer: (A) -8 (B) -5 (C) -2 (D) -1

Bytelearn · Accepted Answer

Find equation of first line: First, let's find the equation of the first line with a slope of 1 that passes through the point (3,0). The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since the slope (m) is 1 and the line passes through (3,0), we can substitute these values into the equation to find b. y = mx + b 0 = (1)(3) + b 0 = 3 + b b = -3 So, the equation of the first line is y = x - 3.Find equation of second line: Next, let's find the equation of the second line with a slope of -(1/4) that passes through the point (-7,0). Again, using the slope-intercept form y = mx + b, we substitute the slope and the point into the equation to find b. y = mx + b 0 = -(1/4)(-7) + b 0 = 7/4 + b b = -7/4 So, the equation of the second line is y = -(1/4)x - 7/4.Find intersection point: Now, to find the intersection point (a,b) of the two lines, we set their equations equal to each other since at the point of intersection, their y-values will be the same. x - 3 = -(1/4)x - 7/4 To solve for x, we combine like terms. x + (1/4)x = -7/4 + 3 (5/4)x = 5/4 x = (5/4) / (5/4) x = 1Find coordinates of intersection point: Having found the x-coordinate of the intersection point, we now substitute x = 1 into either of the line equations to find the y-coordinate. We'll use the first line's equation for simplicity. y = x - 3 y = 1 - 3 y = -2 So, the intersection point (a,b) is (1,-2).Find value of a + b: Finally, we find the value of a + b. a + b = 1 + (-2) a + b = -1

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