Hello!
Let's write the points here:
• A = (-4, -3)
,• B = (1, 2)
First, we have to calculate the slope of this line, using the formula:
[tex]\text{Slope}=\frac{y_B-y_A}{x_B-x_A}[/tex]Let's replace the values in the formula:
[tex]\text{Slope}=\frac{2_{}-(-3)_{}}{1-(-4)_{}}=\frac{2+3}{1+4}=\frac{5}{5}=1[/tex]So, the slope of this line will be 1.
Now, let's write the equation in the point-slope form:
[tex]y-y_{1}=m\mleft(x-x_{1}\mright)[/tex]We can choose any point to replace in (x1, y1). I'll use point A:
[tex]\begin{gathered} y-(-3)=1\mleft(x-(-4)\mright) \\ y+3=1(x+4) \end{gathered}[/tex]To finish, the equation in slope-intercept form:
[tex]y=mx+b[/tex]Let's replace using the point B and m = 1:
[tex]\begin{gathered} 2=1\cdot1+b \\ 2=1+b \\ 2-1=b \\ b=1 \end{gathered}[/tex]So, the equation in the slope-intercept form is:
y = 1x +1
Answer:• Equation in point-slope form: ,y+3=1(x+4)
,• Equation in slope-intercept form: ,y = 1x +1
