Question

: How do you write an equation for each line in point-slope form and slope-intercept form if slope =4, passing through \[\left( 1,3 \right)\]?

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 answer:
We are asked to find the equation of the straight line with slope value as 4 and which passes through \[\left( 1,3 \right)\]. We will use the slope intercept form of the equation of a straight line for which the value of m is 4. 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 in the slope intercept form of the equation, we get
\[\Rightarrow y=4x+b\]
This equation still has an unknown constant. To find the value of this constant, we will use the other information about the line. As the line passes through the point \[\left( 1,3 \right)\], this point must satisfy the equation of the line. Substituting the point in the equation, we get
\[\Rightarrow 3=4(1)+b\]
Solving the above equation, we get
\[\Rightarrow b=-1\]
Now we have values of both m and b, hence, the slope intercept form of the equation is \[y=4x-1\].
We can also graph the equation as follows:

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.