Write the equation of the line of slope 10 through the point one, negative two in the form 𝑦 equals 𝑚𝑥 plus 𝑐.
We’re given the form 𝑦 equals 𝑚𝑥 plus 𝑐. In this form, we know that our 𝑚 represents slope. Our question tells us that our slope equals 10. So we can substitute 10 for 𝑚.
We also have one point; one, negative two that we can substitute here for an 𝑥 and 𝑦. Now we have negative two equals 10 times one plus 𝑐. We use this information to solve for 𝑐. 10 times one equals 10, and we bring our negative two down.
To solve for 𝑐, we’ll subtract 10 from both sides of our equation. Negative two minus 10 equals negative 12. And on the right side of the equation, we’re left with 𝑐. 𝑐 equals negative 12.
What we need to do now, is take the information we have and put it in slope intercept form, 𝑦 equals 𝑚𝑥 plus 𝑐. We plug in 10 for our slope and negative 12 for the 𝑐 variable, which can be reduced to 𝑦 equals 10𝑥 minus 12.