Question

How do you write an equation of the line given \[m=-3\And b=5\]?

Answer 1

Hint: There are many forms to express the equation of a straight line, one of them is the slope-intercept form. The slope intercept form of a line is \[y=mx+b\], here m is the slope of the line and b is the Y-intercept of the line. We can find the equation of the line by substituting values of the m, and b in the given equation.

Complete step by step solution:
We are asked to find the equation of the straight line with given slope and Y-intercept values. As we are given both slope and Y-intercept, we will use the slope intercept form of the equation of a straight line for which the value of m and b are \[-3\And 5\] respectively. The slope intercept form of the equation is \[y=mx+b\] here m is the slope of the line and b is the Y-intercept of the line.
Substituting the values of the variables m, and b in the slope intercept form of the equation, we get
\[\Rightarrow y=(-3)x+5\]
Simplifying the above equation, we get
\[\Rightarrow y=-3x+5\]
Hence, the slope intercept form of the equation is \[y=-3x+5\]. From the equation, we can say that the line has a slope of 2, and its Y-intercept equals \[-3\].
We can also graph the equation as

Note: We can express the straight line in its different forms like standard form, intercept form etc. using the slope intercept form of the equation. The standard form of the equation of a straight line is \[ax+by+c=0\]. And the intercept form of the equation of straight line is \[\dfrac{x}{a}+\dfrac{y}{b}=1\], for this form a, and b are X-intercept and Y-intercept respectively.