adkor95
Bunuel
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?
\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).
So we are asked to find the value of \(m\).
(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.
(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.
Answer: A.
Thanks! But is this implying that no matter the format of the equation, the term/number multiplying the x-value is the gradient? I was thrown off by '+ 1' in the equation.
Yes, m, the co-efficient of x in the equation of this format y = mx + c gives the slope of the line.
y = 3x + 2
y = 3x - 1
Both have the same slope 3. They are parallel lines.
Check the concepts of Graphing here:
https://youtu.be/3kX5UtvHGFg