The equation of line in slope intercept form is y=(7/4)x-13 and the y-intercept is b=-13.
Given that a line is passes through the point (4,-6) and the slope is m=7/4.
We want a line that passes through (4,-6) and the slope is m=7/4.
To find the equation of a line we want to write the equation in the form y=mx+b where m is the slope and b is the y-intercept.
Given that the m=7/4.
The given point is (x₁,y₁)=(4,-6).
Now, we will write our equation by using the point-slope form. The point-slope form is:
y-y₁=m(x-x₁)
Now, we will substitute the values to find new equation, we get
y-(-6)=(7/4)(x-4)
y+6=(7/4)(x-4)
Further, we will apply the distributive property a(b+c)=ab+ac, we get
y+6=(7/4)x-(7/4)4
y+6=(7/4)x-7
Now, we will subtract 6 from both sides, we get
y+6-6=(7/4)x-7-6
y=(7/4)x-13
Hence, the equation of line in slope intercept form where a line that passes through (4,-6) and the slope m=7/4 is y=(7/4)x-13 and the y-intercept form is b=-13.
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