Question

Calculate the value of m if the line 3x-my-19 makes an angle of 45 degree with the line 3x+5y=7​

a) m=5
b) m=3
c) m=−5
d) m=−3

Answer 1

To find the value of m, rearrange the equation for the given line into slope-intercept form and compare the slopes with the line 3x+5y=7. The value of m is -3.

Step-by-step explanation:

To find the value of m, we need to compare the slopes of the given line and the line 3x+5y=7. The slope of the given line can be found by rearranging the equation into slope-intercept form:

3x - my - 19 = 0

-my = -3x + 19

y = (3/m)x - (19/m)

Comparing this with 3x + 5y = 7, we can see that the slope of the given line is 3/m. Since we know that the two lines make an angle of 45 degrees, the slopes must be negative reciprocals. Thus:

3/m * -1 = -1/3

Solving for m, we find:

m = -3