Given the equation of the line :
[tex]7x+3y=42[/tex]To find the slope, we will write the equation of the line in slope- intercept form
So, it will be as following :
[tex]\begin{gathered} 7x+3y=42 \\ 3y=-7x+42 \end{gathered}[/tex]Divide all terms by 3
[tex]\begin{gathered} \frac{3y}{3}=-\frac{7x}{3}+\frac{42}{3} \\ \\ y=-\frac{7}{3}x+14 \end{gathered}[/tex]Which will be similar to the general form: y = m * x + b
Where m is the slope
So, the slope of the given equation = -7/3
To find y- intercept, substitute with x = 0
[tex]\begin{gathered} 7\cdot0+3y=42 \\ 3y=42 \\ \\ y=\frac{42}{3}=14 \end{gathered}[/tex]To find x- intercept , substitute with y = 0
[tex]\begin{gathered} 7x+3\cdot0=42 \\ 7x=42 \\ \\ x=\frac{42}{7}=6 \end{gathered}[/tex]so, the answer is :
[tex]\begin{gathered} x-\text{intercept}=6 \\ y-\text{inercept}=14 \\ \text{slope}=-\frac{7}{3} \end{gathered}[/tex]