PHS Algebra 56

Linear Equation is y = mx + b

"m" represents the slope. "b" represents the y-intercept.

. How to Graph Using y = mx + b Solve the equation for y. Determine the slope and y-intercept. Graph the y-intercept. Use the movements of slope (or rise/run) to graph more points begainning at the y-intercept. Connect the points with a straight line and arrows on each end. Label the line with its equation.

The lines intersect at zero points. (The lines are parallel.)

The lines intersect at exactly one point. (Most cases.)

The lines intersect at infinitely many points. (The two equations represent the same line.)

The slope of a line tells us how something changes over time. If we find the slope we can find the rate of change over that period.

e was saving per month. This is called the rate of change per month.

John may want to analyze his finances a little more and figure out about how much h

Solve. 14 – 3y = 4y

Add 3y to each side

Simplify both sides.

Use properties of equality together to isolate variables and solve algebraic equations.

Subtract 2 from both sides of the equation to get the term with the variable by itself.

Problem Solve 3y + 2 = 11.

In this lesson you will learn how to solve equations by using inverse operations

Solving linear equations with no solutions and with infinite solutions, using inverse operations, the distributive property, including equations with variables on both sides

The distributive property is telling us how to deal with those parenthesis when we just have letters inside

t's called the point-slope formula (Duh!)

You are going to use this a LOT!

The word slope (gradient, incline, pitch) is used to describe the

measurement of the steepness of a straight line.

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

Many problems lend themselves to being solved with systems of linear equations. In "real life", these problems can be incredibly complex. This is one reason why linear algebra (the study of linear systems and related concepts) is its own branch of mathematics. In your studies, however, you should generally be faced with much simpler problems. What follows are some typical examples.

Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:

  a point  a slope

ALWAYS!

Find the slope

Using this formula, when we know: one point on the line and the slope of the line,

This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.

y = mx + b

y = mx + b (–6) = (4)(–1) + b –6 = –4 + b –2 = b