Desmos Tricks

Linear Equations Mastery

Why solve for \(y\) when Desmos can handle the raw equations? Here is how to hack every form.

Desmos 4-Form Mastery

slope-intercept Form 1: Regression Hack

A line passes through the points \((-1, -1)\) and \((1, 3)\). What is the equation of the line?

(A) \(y = x + 1\)

(B) \(y = 2x + 1\)

(D) \(y = 3x\)

Don't calculate slope. Use Regression.

1. Add a table in Desmos. Enter \((-1, -1)\) and \((1, 3)\).

2. Type y_1 ~ mx_1 + b.

Desmos tells you m=2 and b=1. The equation is \(y=2x+1\). The answer is (B).

point-slope Form 2: Direct Entry

A line passed through \((3, 5)\) and has a slope of \(2\). Which graph represents this line?

(A)

(B)

(C)

(D)

Use the Point-Slope Formula directly.

The Point-Slope Form is:

\( y - y_1 = m(x - x_1) \)

Given the point \((3, 5)\) and slope \(m=2\), just plug them in:

Step 1: Identify \(x_1=3\), \(y_1=5\), and \(m=2\).
Step 2: Substitute into the formula: \( y - 5 = 2(x - 3) \).
Step 3: Type this exact equation into Desmos.
Step 4: Match the graph Desmos draws with the correct option below.

The graph will pass through \((3, 5)\) and have a 2. Option (A) is the correct match.

standard form Form 3: Slope Hack

What is the slope of the line \(3x + 4y = 12\)?

(A) \(3/4\)

(B) \(-3/4\)

(D) \(-4/3\)

Don't solve for y.

Type 3x + 4y = 12. Look at the intercepts.

Rise/Run from \((0, 3)\) to \((4, 0)\) is down 3, right 4. Slope = \(-3/4\).

PRACTIX MATH PILLAR ⚡ LIGHTNING FAST

School Way (Slow)

Subtract \(Ax\), divide by \(B\), simplify for slope...

Practix Way (Fast)

\[ m = -\frac{A}{B} \]

In \(3x + 4y = 12\), since \(A=3\) and \(B=4\), the slope is \(-3/4\). Done in 1 second.

intercept form Form 4: Visual Check

Which equation has an x-intercept of 3 and a y-intercept of 4?

(A) \(\frac{x}{3} + \frac{y}{4} = 1\)

(B) \(\frac{x}{4} + \frac{y}{3} = 1\)

Use Regression for Intercepts.

Instead of manual entry, use regression to find \(a\) and \(b\). Type this exactly:

                                        x_1/a + y_1/b ~ 1
                                    

Desmos instantly finds a=3 and b=4. No math required. Done.

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